The concept of interaction consistency for not necessarily
Lagrangian theories has been developed in [1]}. This paper
tells us that the non-Lagrangian interaction is consistent if the
non-linear theory admits the same number of (i) gauge symmetries,
(ii) gauge identities, and (iii) physical degrees of freedom as a
free model. All these fact are easily verified. At first, the
equations of motion (REF ) are preserved by the Yang-Mills
gauge symmetry,
\(\phantom{\frac{1}{2}}\delta _\zeta \mathcal {A}_\mu =D_\mu \zeta \,,\qquad \delta _\zeta \mathbb {T}_\mu =[\,\zeta \,,\mathbb {T}_\mu ]\,,\phantom{\frac{1}{2}}\) 
